Reddy A.

asked • 09/01/19

Prove or Disprove this statement

There exists a prime number x such that x + 16 and x + 32 are also prime numbers

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Inactive Tutor answered • 09/01/19

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21 is the prime# you're looking for because 37 and 53 are also prime.

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21 is not prime
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09/24/19

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Disproved: if x is prime, x mod 3 must be 1 or 2. But (x + 16) mod 3 is then 2 or 0 respectively, and (x+32) mod 3 is 0 or 1, respectively. Thus, one of { x, x+16, x+32 } is always divisible by 3 and therefore at least one of the three numbers is composite.
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09/24/19

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